Help to get rid of fleas?

A few months ago (about beginning of the year…) I got a new kitten, and I believe he came into the house with fleas, I had bathed him and given him a treatment(Advantage(?) II) which seemed to kill them off mostly if not fully. I moved out a few weeks ago, and moved in with some other family, and so I’m not sure about giving him a bath here, due to the fact they don’t have a really good area to bathe him, as his fleas are bad again. I had been giving him advantage ll, but for a little while I wasn’t able to (the last month or so), so they’re back full force.

Currently I haven’t noticed any on me, but I combed him a maybe an hour ago and pulled up a good three or four after one swipe of the comb. (Had been just getting some loose fur off, and discovered the fleas)

Does Advantage (or really any of the flea treatments, if one works better let me know please…) help to kill them off like a bath does? Or do I need to figure out a way to bathe him?

Sorry if my post seems a bit silly, he’s my first cat that I’m solely responsible for, so I really don’t know much about how the flea treatments work… let alone how to handle fleas.

I did see a post a little ago about vacuuming, and washing my bedding, but I don’t know how often I’m supposed to do that. Any advice or tips you guys have would be so appreciated and helpful to me!! Thank you in advance